The Bevel and the Rule
Introduction
The cartabón (from Italian quartabono[1] or from Occitan escartabont[2]) is a template in the shape of a scalene right triangle that is used in technical drawing.[3] They can be of different sizes and have a graphic scale, to be used as a measuring instrument. Two bevels form an equilateral triangle, whose 3 angles are 60⁰. By dividing it into two equal triangles, the angles of 90°, 60° and 30° are formed. It is usually used, together with a square or a ruler, to draw parallel, perpendicular or lines with various angles. It can be made of different materials, although the most common and useful is transparent plastic.
Uses
We can use the bevel to:
Shape and dimensions
A bevel is shaped like a scalene right triangle, and has neither equal sides nor angles. If we put two bevels together by their longest leg, they form an equilateral triangle, this property being what determines the measurements of its sides and angles.
The hypotenuse is twice as long as the short leg.
Knowing that:
and by the Pythagorean Theorem, we have that:.
With what we have:
If we take the small leg as a unit making b = 1, we have that the hypotenuse measures 2 and the larger leg measures 2.
Knowing that:
Its greatest acute angle measures 60°, and its smallest 30°.
Use of the bevel
Given the shape of the bevel in the isometric perspective, among other uses of technical drawing, as we can see.
Placing the ruler horizontally at the right angle of the bevel allows you to draw vertical lines. The 30° angle allows the axes of the horizontal plane to be drawn.
If we put the coordinates of a point on these three axes, drawing the corresponding parallels to the axes, we can locate it in space, according to the isometric perspective.
In the case of the military perspective, the use of the bevel is similar to the isometric: the is vertical, the forms an angle of 30° with the horizontal, and the is perpendicular to the ; that is, it forms an angle of 60° with the horizontal. Therefore, they coincide with the characteristics of the bevel, as we can see.